Finite Group Databasebeta

← Prev (#46831398) Next (#46831400) →

C3⋊AGL(1,𝔽7)×C11⋊C25 #46831399

order34650
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3⋊AGL(1,𝔽7)×C11⋊C25
unambiguous semidirect productC3⋊(AGL(1,𝔽7)×C11⋊C25)
unambiguous semidirect productΓL(1,𝔽8)⋊(D3×C11⋊C25)
unambiguous semidirect productD21⋊(C3×C11⋊C25)
unambiguous semidirect product(C11×C3⋊AGL(1,𝔽7))⋊C25
unambiguous semidirect product(D21×C11⋊C25)⋊C3

Splittings

derivedC3×C7×C11 ⋊ C2×C3×C25
HallC3×ΓL(1,𝔽8)×C11⋊C25 ⋊ C2
HallC7×C11⋊C25 ⋊ C3×D3
HallC11×C3⋊AGL(1,𝔽7) ⋊ C25
HallC3×C11×ΓL(1,𝔽8) ⋊ C2×C25
HallC7×C11 ⋊ C3×D3×C25
HallC3×ΓL(1,𝔽8) ⋊ C2×C11⋊C25
SylowC11 ⋊ C25×C3⋊AGL(1,𝔽7)
SylowC7 ⋊ C3×D3×C11⋊C25

Subgroups

subgroupG/H
center, Frattini, hypercenterC5C11⋊C5×C3⋊AGL(1,𝔽7)
commutator, hypocenterC3×C7×C11C2×C3×C25
Fitting, socle, cosocleC3×C5×C7×C11C2×C3×C5
prime radicalC5×C11×C3⋊AGL(1,𝔽7)C5
LCSG ▷ C3×C7×C11
UCSC1 ◁ C5

108 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5775

Conjugacy classes & character table

420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 42);